Various financial service entities and investors buy and sell securities, such as mortgage passthrus, at all times of the trading day and in large quantities and often accumulate large positions in these instruments, either long or short. To counteract adverse price movements, it is often desirable to hedge the positions effectively by the simultaneous purchase or sale of other instruments, for example Treasury bills. An element in formulating a hedging strategy is to determine how much the price of each instrument changes as the yield curve changes. This is referred to herein as the “duration.” Knowing the duration of both the mortgage passthru and the Treasury bill, a trader can determine how much Treasuries to buy or sell to offset the risk of the mortgage position up to the first order. Therefore, a proper estimation of mortgage duration in real-time is often desirable to market-making activity.
However, in the case of mortgage passthrus, determination of duration is not only complicated by the fact that it depends on the inherent optionality of the passthru—mortgage holders have the option to prepay their mortgage at any time—and the degree to which the option is in or out of the money, but also that this optionality changes dynamically as mortgage rates change during the day, sometimes dramatically so. A mortgage passthru is said to be “in-the-money” if its coupon exceeds the prevailing mortgage rate and vice versa. The prevailing mortgage rate is determined in the secondary mortgage market based on the real-time prices of mortgage passthrus across different coupons. This is referred to as the current (or par) coupon rate. The more in-the-money a mortgage passthru is, the shorter its duration and the more out-of-the-money it is, the longer its duration. Because the current coupon changes dynamically, so does the optionality of the passthru and thus its duration.
Several methods exist to determine the duration of a mortgage. Most are model based, where market participants typically derive statistical models of mortgage prepayment behavior and thus determine price changes as rates change. However, despite the care and effort that goes into modeling these, there is wide variability in the outputs of these models, and because their overall consensus is likely reflected in the traded prices, there is a need for deriving the mortgage duration empirically from actual prices and observed rate changes. There is also a need for determination of empirical durations of mortgage passthrus in real-time for the dynamic hedging of large and heterogeneous mortgage passthru positions.